Multimode fiber optic rotation sensor

ABSTRACT

A fiber optic rotation sensor comprises a length of multimode optical fiber 11, forming a sensing loop 16 for sensing rotation in accordance with the Sagnac effect. Nonrotationally induced phase errors in the detected optical signal reduced or eliminated by (a) utilizing a light source 10 which produces light having a coherence length which is less than the difference in optical path length between modes; (b) utilizing a sufficiently large detector 20 so that substantially the entire optical output signal is intercepted by such detector; and (c) coupling light to the multimode fiber so that the electric field amplitudes in each of the modes are substantially equal.

The United States Government has rights in this invention pursuant tocontact F49620-80-C-0040 awarded by the United States Air Force Officeof Scientific Research.

This patent application is a continuation-in-part of our copendingUnited States patent application, Ser. No. 318,813, filed Nov. 6, 1981,now U.S. Pat. No. 4,456,377 entitled "Multimode Fiber Optic RotationSensor".

BACKGROUND OF THE INVENTION

The present invention relates to fiber optic rotation sensors, andparticularly to a fiber optic rotation sensor employing a Sagnacinterferometer with a multimode fiber sensing loop.

Fiber optic rotation sensors typically comprise a loop of fiber opticmaterial to which light waves are coupled for propagation around theloop in opposite directions. Rotation of the loop creates a phasedifference between the counter propagating waves, in accordance with thewell-known "Sagnac effect", with the amount of phase differencecorresponding to the velocity of loop rotation. The counterpropagatingwaves, when recombined, interfere constructively or destructively toproduce an optical output signal which varies in intensity in accordancewith the rotation rate of the loop. Rotation sensing may be accomplishedby detection of this optical output signal.

Accurate detection of the rotationally induced Sagnac phase differencerequires that nonrotationally induced phase differences, caused by thephysical properties of the fiber (e.g. fiber birefringence), besubstantially eliminated, since such phase differences areindistinguishable from the Sagnac phase difference, and thus, mayprovide a "phase error" in the optical output signal. If the opticalpaths for the counter propogating waves are identical when the loop isat rest, so that these nonrotationally induced phase differences areeliminated, the interferometer is said to be "reciprocal", while if theyare not identical, the interferometer is said to be "nonreciprocal".

Nonreciprocity in fiber optic interferometric rotation sensors is causedby two factors. First, an optical fiber may support many differentfundamental or spatial modes, e.g., the HE₁₁ mode, the TE₁₀ mode, etc.,each of which has a different propagation velocity or phase velocity.(For the present discussion, a mode may be viewed as a particularoptical path through the fiber.) Second, the birefringence of an opticalfiber is not uniform along the fiber, and thus, coupling of light energybetween the modes exists. The presence of both of these factors causeseach of the counterpropagating waves to travel different optical pathsaround the fiber loop, so that when they are recombined, there is aphase difference therebetween. This phase difference, which may beseveral orders of magnitude larger than the Sagnac phase difference, isindistinguishable from the rotationally induced Sagnac phase difference,and thus, manifests itself as an error in the optical output signal. Itshould be emphasized that neither of the above two factors takenindividually is sufficient to destroy reciprocity. Both factors must bepresent to yield nonreciprocal operation.

The prior art has endeavored to satisfy the reciprocity requirement byutilizing single mode fibers, which have only one fundamentalpropagation mode, namely, the HE₁₁ mode. Although use of a single modefiber would theoretically eliminate the first factor, and thus, providereciprocity, it has been found that, in practice, a single mode fiberhas two orthogonal polarization modes which are nearly degenerate, i.e.,they have slightly different propagation phase velocities. Suchdifference in propagation velocities, while quite small, is neverthelesssufficient to cause nonreciprocal operation of single mode fiberrotation sensors. This problem has been solved in the prior art, e.g.,by utilizing a fiber optic polarizer to block one of the twopolarization modes of the single mode fiber as described in an articleby R. Ulrich and M. Johnson, entitled "Fiber Ring InterferometerPolarization Analysis", in Optics Letters, Vol. 4, pp. 152 (April 1979).

There has been little, if any, attention directed towards the use ofmultimode fibers for rotation sensing, because of the large number ofmodes and different propagation velocities. While the difference inpropagation velocities between modes can be reduced by utilizing agraded index multimode fiber, as opposed to a step index multimodefiber, the difference in propagation velocities for either type of fiberis sufficiently large that multimode fibers have heretofore beenconsidered unsuitable for use in rotation sensors. Moreover, the problemis further complicated by the fact that, within each of the fundamental(i.e. spatial) modes of a multimode fiber, there exists a set of modepatterns, referred to herein as "generalized polarization modes", havingpropagation velocities which are nearly, but not exactly, equal. Thedifference in propagation velocities between the generalizedpolarization modes of a particular fundamental mode are typically on thesame order of magnitude as the difference in propagation velocitiesbetween the fundamental modes of a graded index multimode fiber. Becauseof the many modes involved (thousands in some cases), and theirassociated propagation velocities, it has heretofore been consideredimpossible, or at least impractical, to achieve reciprocal operation ina Sagnac interferometric rotation sensor utilizing a single multimodefiber.

SUMMARY OF THE INVENTION

The rotation sensor of the present invention comprises a single,continuous strand of multimode optical fiber, forming a loop, in aSagnac interferometer configuration. A fiber optic directional coupleris used to close the loop and couple a pair of counter propagating lightwaves to the loop. The coupler recombines the counter propagating lightwaves after traverse of the loop to form an optical output signal whichis impressed upon a photodetector. Rotation of the loop induces a phasedifference between the counter propagating waves which causes themagnitude of the optical output signal to vary in accordance with therate of rotation. By detecting the optical output signal, a directindication of the rotation rate may be obtained.

It has been found that phase errors in the optical output signal, causedby nonrotationally induced phase differences between thecounterpropagating waves, may be systematically reduced or eliminated by(1) utilizing source light having a coherence length which is less thanthe difference in optical path length between propagation modes; (2)utilizing a sufficiently large detector so that substantially the entireoptical output signal is impressed upon the detector surface; and (3)coupling light to the multimode fiber so that the electric fieldamplitudes in each of the propagation modes are substantially equal.Such elimination or reduction of phase errors permits detection of therotationally induced Sagnac phase difference, yielding a practical,usable multimode rotation sensor.

The multimode fiber rotation sensor of the present invention issurprisingly stable and relatively insensitive to variations in fiberbirefringence caused by environmental factors, such as temperature orvibration. Phase changes and coupling between modes due to suchvariations in fiber birefringence tend to be averaged over the modes sothat the overall effect of the environmental factors upon the opticaloutput signal is quite small. The stability of the optical output signalis a function of the number of modes, and thus, it is preferable to usea fiber which supports a large number of modes. In this regard, a stepindex multimode fiber may be preferred for use in the present invention,since a step index fiber is capable of supporting more modes than agraded index fiber of comparable size.

The multimode fiber rotation sensor of the present invention hassignificant advantages over current state of the art single mode fiberrotation sensors. One of the most important advantages is that thepresent invention is much less expensive to fabricate, since multimodefibers and multimode components (e.g. couplers) are less costly andeasier to work with than are single mode fibers and components.Moreover, since spatially incoherent light may be used, the rotationsensor can utilize an inexpensive light emitting diode (LED) as asource, rather than an expensive high spatial coherence length laser.

Another advantage is that the multimode fiber sensing loop has lesssusceptibility to the Kerr effect, since, in the present invention, thiseffect is spatially averaged over a large number of modes. Anotherreason for such reduced susceptibility is that the larger diameter coreof a multimode fiber results in a lower optical intensity in the fiber.Further, multimode fiber is less sensitive to the Faraday effect, whichmay be induced by external magnetic fields, since the modalbirefringence of the fiber is high compared to birefringence induced bythe Faraday effect. In essence, the multimode fiber's linearbirefringence overwhelms the circular birefringence induced by theFaraday effect. Finally, the multimode rotation sensor, like itscounterpart single mode sensor, can be fabricated as an all fibersystem, utilizing a single, continuous strand of fiber optical material.

In a second embodiment of the present invention, a modal filtercomprising a transmissive hologram is used to eliminate theabove-described nonrotationally induced phase errors. This holographicfilter is arranged so that source light passes through the filter onceon its way to the loop, and again on its way to the detector, so thatonly a single mode of the multimode fiber is utilized.

These and other features of the present invention may be more fullyunderstood through reference to the drawings.

DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic drawing of the rotation sensor of the presentinvention, showing a single, continuous strand of optical fiber, towhich light from a light source is coupled, and showing the multimodesensing loop, formed from such single, continuous strand; in addition,FIG. 1 shows a detection system for detecting the phase differencebetween waves counterpropagating through the fiber loop;

FIG. 2 is a schematic drawing illustrating a conceptual model of thefiber loop 16, showing, for an exemplary pair of modes, the electricfield components of the counterpropagating waves as they traverse thefiber loop;

FIG. 3 is a schematic drawing of the conceptual mode of FIG. 2, showingthe electric field components of the counterpropagating waves after theyhave traversed the fiber loop;

FIG. 4 is a vector diagram of the optical output signal, showing avector directed along the real axis, which represents the vector sum ofthe "dc" terms resulting from the electric field components shown inFIG. 3, and another vector, rotating in the manner of a phasor, whichrepresents the vector sum of the interference terms resulting from theelectric field components shown in FIG. 3, and further illustrating theresponse of the vector representing the interference terms to (1) therotationally-induced Sagnac phase difference, and (2) phase errorscaused by non-rotationally induced phase differences;

FIG. 5 is a graph, corresponding to the vector diagram of FIG. 4, of theoptical intensity, as measured by the detector, versus the Sagnac phasedifference, illustrating the effect of non-rotationally induced phaseerrors;

FIG. 6 is a vector diagram of the interference terms resulting fromGroup III electric field components;

FIG. 7 is a vector diagram showing a resultant vector which representsthe vector sum of the two vectors of FIG. 6, and illustrating the phaseerror associated with such resultant vector sum;

FIG. 8 is a vector diagram showing the vectors of FIG. 6 equalized inmagnitude;

FIG. 9 is a vector diagram of a resultant vector, which represents thevector sum of the vectors of FIG. 8, illustrating that phase errors maybe eliminated by equalizing the magnitudes of the vectors.

FIG. 10 is a schematic drawing of the fiber portion which extendsbetween the couplers of FIG. 1, showing this fiber portion severed, andshowing a modal filter comprising a transmissive holograph, interposedtherebetween; and

FIG. 11 is a schematic drawing illustrating a technique for making thetransmissive holographic filter of FIG. 10.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In the preferred embodiment, shown in FIG. 1, the rotation sensor of thepresent invention comprises a light source 10 for introducing a CW lightwave into a single, continuous length or strand of multimode opticalfiber 11. As used herein, "multimode fiber" means that the fibersupports plural fundamental modes for the particular source light used,as opposed to single mode fiber which supports only one fundamentalmode. The fiber 11 passes through ports, labeled A and C, of a firstdirectional coupler or splitting device 12, and through ports, labeled Aand C of a second directional coupler or splitting device 14. Thus, thefiber 11 extends from the light source 10 to port A of the coupler 12and extends from port C of the coupler 12 to port A of the coupler 14.The portion of the fiber 11 extending from port C of the coupler 14 iswound into a loop 16. By way of specific example, the loop 16 maycomprise 1,000 turns, each bounding an area of about 150 sq. cm. The endof the fiber 11, from the loop 16, is passed through ports, labeled Dand B, of the coupler 14, with port D adjacent to the loop 16. A smallportion 17 of the fiber 11 extends from port B of the coupler 14 andterminates nonreflectively, without connection.

A second length of fiber 19 is passed through the ports labeled D and Bof the coupler 12. The portion of the fiber 19 projecting from port Dterminates nonreflectively, without connection. However, the portion ofthe fiber 19 projecting from port B of the coupler 12 is opticallycoupled to a photodetector 20, which produces an output signalproportional to the intensity of the light impressed thereon.

The present invention also includes detection electronics 22, comprisinga lock-in amplifier 24, a signal generator 26, and a phase modulator 28.By way of specific example, the phase modulator 28 may comprise a PZTcylinder, having a diameter of e.g. about 1 to 2 inches, about which aportion of the fiber loop 16 is wrapped, e.g., 4 to 10 times. The fiberis bonded to the PZT cylinder 28 by a suitable adhesive, so that thefiber 11 will be stretched upon radial expansion of the cylinder 28. Inthis regard, the phase modulator 28 is driven by an AC modulatingsignal, having a frequency in the range of, e.g., 10-100 kHz, which isprovided on a line 30 from the signal generator 26. For proper operationof the detection electronics 22, it is important that the phasemodulator 28 be located on one side of the loop 16, e.g., adjacent tothe port D of the coupler 14, rather than at the center of the sensingloop 16.

The AC modulation signal from the generator 26 is also supplied on aline 32 to the lock-in amplifier 24. A line 34 connects the lock-inamplifier 24 to receive the detector 20 output signal. The amplifierutilizes the modulation signal from the generator 26 as a reference forenabling the amplifier 24 to synchronously detect the detector outputsignal at the modulation frequency. Thus, the amplifier 24 effectivelyprovides a band pass filter at the fundamental frequency (i.e., thefirst harmonic frequency) of the phase modulator 28, blocking all otherharmonics of this frequency. It will be understood by those skilled inthe art that the magnitude of this harmonic component of the detectoroutput signal is proportional, through an operating range, to therotation rate of the loop 16. The amplifier 24 outputs a signal which isproportional to this first harmonic component, and thus, provides adirect indication of the rotation rate.

Additional details of the detection electronics 22 are described ininternational patent application No. PCT/US 82/00400 published Oct. 14,1982, as publication No. WO 82/03456, and entitled "Fiber Optic RotationSensor", which is incorporated herein by reference. This detectionsystem is also described in Optics Letters, Vol. 6, No. 10, (October1981) pp. 502-504. Another detector system which is suitable for use inthe present invention is described in an article authored by J. L. Davisand S. Ezekiel, published in SPIE, Vol. 157, Laser Inertial RotationSensors (1978), pp. 131-136.

It is believed that the type of multimode fiber utilized for the fiber11 is not critical to operation of the present invention. Thus, stepindex, as well as graded index, multimode fibers may be used. However,the performance of the rotation sensor, in terms of its susceptibilityto environmental influences, such as temperature and vibration, appearsto be a function of the number of modes. Thus, a step index multimodefiber, which is capable of supporting more modes than a comparably sizedgraded index fiber, may be preferable. In the embodiment shown, thefiber 11 comprises a step index multimode fiber having a core diameterof about 50 microns, and the fiber 19 is identical to the fiber 11.

A fiber optic directional coupler, suitable for use as the couplers 12and 14, is disclosed in U.S. Pat. No. 4,136,929, issued Jan. 30, 1979 toSuzaki, which is hereby incorporated by reference herein. As shown inFIGS. 3a to 3d of this patent, the coupler comprises a pair of blockshaving arcuate grooves in which respective multimode fibers are mounted.The surfaces of the blocks are cut and polished so that the cladding anda portion of the core are removed from one side of the fiber. Thesurfaces of the blocks are then placed together in face to facerelationship, with the exposed core portions of the fibers juxtaposed.Preferably, the couplers 12 and 14 of FIG. 1 each have a coupling ratioof 50 percent so that light introduced into port A is evenly splitbetween ports C and D. The rotation sensor of FIG. 1 may also beconstructed from bulk optic components by substituting beam splittersfor the couplers 12, 14.

The light source 10 is important to proper operation of the presentinvention. Specifically, the source 10 should provide light which ishighly incoherent, so that the relative phases of light in each of themodes of the fiber are essentially random with respect to each other. Inaddition, the light should be coupled to the fibers so that the electricfield amplitudes for each mode are equal in magnitude. As discussedhereinafter, to the extent that both of these requirements aresatisfied, certain types on nonrotationally induced phase errors will beeliminated. A preferred light source for use as the source 10 is asurface emitting type light emitting diode (LED), having a wavelength onthe order of 700 to 900 nm. Since an LED is an extended source, it tendsto launch each mode with an equal light intensity. Further, the lightproduced by an LED is highly incoherent. It should be noted that, ingeneral, an LED is particularly desirable for use as a light source,since it is relatively inexpensive compared to lasers.

As an alternative, incoherent light may be generated utilizing acoherent light source by providing a phase modulator 40 adjacent to thesource 10, as shown in phantom lines in FIG. 1. The modulator 40 may beof the same type as the modulator 28, e.g., a PZT cylinder about whichthe fiber 11 is wrapped. The modulator 40 may be driven by a signalgenerator (not shown) which produces either a random signal or a highfrequency signal, above the detection bandwidth of the electronics 22.The operating frequency of this signal generator, however, should bedifferent than that of the signal generator 26. Moreover, it isimportant that the modulation be accomplished prior to reaching the loop16; otherwise such modulation will tend to average the rotation signalto zero.

In addition to providing incoherent light, the modulator 40 may alsoserve as a mode scrambler to distribute light evenly among the modes ofthe fiber. In essence, wrapping the fiber, e.g., 5-10 times around arelatively small diameter (e.g., 1/2-1 inch) PZT cylinder causessufficient coupling between the modes to substantially equalize thefield amplitudes among the modes.

The photodetector 20 is also of critical importance to proper operationof the rotation sensor. Specifically, the photodetector should have asufficiently large surface area to intercept substantially all of thelight exiting the fiber 19, when positioned normal to the fiber axis.The diameter of the photodetector 20 is typically in the range of 2-10millimeters, the exact size depending upon the diameter of the multimodefiber 19, the numerical aperture of the fiber 19 (which defines thedivergence of the light as it exits the fiber 19) and the distancebetween the end of the fiber 19 and the photodetector 20. In theembodiment shown, the photodetector 20 is a standard PIN or AvalancheSilcon Photodiode, having a diameter of 10 millimeters.

In operation, a continuous light wave W_(i) is input from the lightsource 10 for propagation through the fiber 11. As the wave W_(i) passesthrough the coupler 12, a portion of the light (e.g. 50 percent) is lostthrough port D. The remaining light propagates from port C of thecoupler 12 to the coupler 14, where the light is split evenly into twowaves W₁, W₂, which propagate in opposite directions about the loop 16.After traverse of the loop 16, the waves W₁, W₂ are recombined by thecoupler 14 to form an optical output signal W₀. A portion of therecombined wave W₀ may be lost through the port B of the coupler 14,while the remaining portion travels from port A of the coupler 14 toport C of the coupler 12, where it is again split, with a portionthereof (e.g., 50%) transferred to the fiber 19. Upon exiting the end ofthe fiber 19, the wave W₀ is impressed upon the photodetector 20, whichoutputs an electrical signal that is proportional to the opticalintensity of the wave W₀.

The intensity of this optical output signal will vary in proportion tothe type (i.e., constructive or destructive) and amount of interferencebetween the waves W₁, W₂, and thus, will be a function of the phasedifference between the waves W₁, W₂. Assuming, for the moment, that thefiber 11 is "ideal" (i.e., that the fiber birefringence is uniform alongits length), measurement of the optical output signal intensity willprovide an accurate indication of the rotationally induced Sagnac phasedifference, and thus, the rotation rate of the fiber loop 16.

As indicated above, present state-of-the-art, multimode fibers are farfrom "ideal", in that (1) they are birefringent, and (2) thebirefringence is not uniform along the length of the fiber, thus,yielding nonrotationally induced phase differences (i.e., phase errors),which are indistinguishable from the rotationally induced Sagnac phasedifference. The present invention utilizes three different techniques toreduce or eliminate these phase errors, namely, (1) use of a sourceproducing highly incoherent light, so that the relative phases of lightlaunched in each of the modes of the fiber are essentially random withrespect to each other, (2) equalizing the electric field amplitudes forlight in each of the modes, and (3) utilizing a detector having arelatively large surface area to capture substantially the entireoptical output signal power. Each of these techniques is directedtowards a particular group or class of phase errors.

Such reduction or elimination of phase errors may be more fullyunderstood through reference to FIG. 2, which depicts a conceptual modelof any two arbitrary modes of a multimode fiber chosen from anyarbitrary set of complete orthogonal modes which allow the descriptionof any propogating field pattern in the multimode fiber as a linearsuperposition of the fields of such set of orthogonal modes. Each modeis assumed to have a propogation velocity different from that of theother modes. Further, to account for the fact that birefringence is notuniformly distributed along the length of the fiber, it is assumed thatthere is coupling of light energy between modes. Such coupling of energywill be referred to herein as "cross coupling."

While it is recognized that, in reality, a mutimode fiber may have e.g.thousands of modes, for the purposes of the present discussion, only twomodes will be considered, it being understood that the two mode case maybe extended to an N mode case, as will be demonstrated mathematicallyhereinafter.

The conceptual fiber model of FIG. 2 will be utilized to represent thesensing loop 16 (FIG. 1). The counterpropagating waves W₁, W₂, areschematically represented as being coupled, by the coupler 14, to theloop 16, by the dashed arrows. The two exemplary, arbitrarily chosenmodes of the multimode optical fiber are schematically represented inFIG. 2 by a first line, connecting a pair of terminals C' and D', and asecond line, parallel to the first line, connecting a second pair ofterminals C" and D". The terminals C' and C" on the left side of FIG. 2correspond the port C of the coupler 14, while the terminals D' and D"on the right side of FIG. 2 correspond to the port D of the coupler 14.The above mentioned first and second lines connecting the terminals willbe used to represent arbitrary modes i and j, respectively, of the fiberloop 16.

Cross coupling between the modes i and j is represented by a pair oflines, labeled "Branch 1" and "Branch 2", respectively. Branch 1represents cross coupling between the terminials C" and D' while branch2 represents cross coupling between terminals C' and D". Theintersection of branch 1 with branch 2, designated by the referencednumeral 50, will be referred to as the "coupling center" although itwill be understood that no coupling exist between the two branches 1 and2. The coupling center 50 is shown as being offset from the center ofthe fiber loop 16 to illustrate that the fiber birefringence is notuniform along its length, and thus, is not symetrically distributedaround the fiber loop 16. Therefore, cross coupled light will travel alonger path in one of the modes than the other, yielding anonrotationally induced phase difference therebetween.

As shown in FIG. 2, the wave of W₁ is coupled to the fiber loop 16 sothat the modes i and j are launched with electric field amplitudes E₁ ⁺and E_(j) ⁺ respectively. Similarily, the wave W₂ is coupled to launcheach of the modes i and j with electric field amplitudes E_(i) ⁻ andE_(j) ⁻, respectively. The plus (+) and minus (-) superscripts designatethe direction of propegation, the clockwise direction about the loop 16being designated by the plus (+) sign, and the counterclockwisedirection around the loop 16 being designated by the minus (-) sign.

As light in each of the modes i and j traverses the fiber loop 16,energy is coupled between the modes, so that each electric field isdivided into two components, namely, a "straight through" component,designated by the subscript "s", and a "cross coupled" component,designated by the subscript "c". Thus, E_(i) ⁺ is divided into astraight through component E_(is) ⁺ which remains in mode i duringtraverse of the loop 16, and a cross coupled component E_(jc) ⁺, whichis cross coupled to mode j during traverse of the loop 16. Similarily,E_(i) ⁻ is divided into components E_(is) ⁻ and E_(jc) ⁻ ; E_(j) ⁺ isdivided into components E_(ic) ⁺ and E_(js) ⁺ ; and E_(j) ⁻ is dividedinto components E_(js) ⁻ and E_(ic) ⁼.

After the light waves have traversed the fiber loop 16, the light atterminal C' will comprise components E_(is) ⁻ and E_(ic) ⁻ ; the lightat terminal C" will comprise component E_(js) ⁻ and E_(jc) ⁻ ; the lightat terminal D' will comprise components E_(is) ⁺ and E_(ic) ⁺ ; and thelight at terminal D" will comprise components E_(js) ⁺ and E_(jc) ⁺, asshown in FIG. 3. These 8 electric field components are combined by thecoupler 14 to form the optical output signal W₀. It will be recognizedby those skilled in the art that, in general, superposition of any twoelectric field components, e.g., E_(is) ⁺ and E_(ic) ⁺ will yield aresultant intensity (I), as measured by the detector 20, which may bedefined as follows:

    I=|E.sub.is.sup.+ |.sup.2 +|E.sub.ic.sup.+ |.sup.2 +2|E.sub.is.sup.+ ||E.sub.ic.sup.+ | cos φ   (1)

where, in this particular example, φ is the phase difference betweenfield components E_(is) ⁺ and E_(ic) ⁺.

The first two terms of equation l(1), namely |E_(is) ⁺ |² and |E_(ic) ⁺|² are steady-state or "d.c." terms, while the last term is an"interference" term having a magnitude depending upon the phasedifference φ between the fields E_(is) ⁺ and E_(ic) ⁺.

In general, all 8 of the above fields E_(is) ⁻, E_(ic) ⁻, E_(js) ⁻,E_(jc) ⁻, E_(is) ⁺, E_(ic) ⁺, E_(js) ⁺ and E_(jc) ⁺, will interfere witheach other to provide an optical intensity at the detector 20 (FIG. 1)comprised of 8 "dc" terms, which are not phase-dependent, and 28"interference" terms which are phase-dependant. The number ofcombinations of phase-dependant terms is actually n(n-1) or 56phase-dependent terms. However, one-half of these terms are simply there-ordered forms of the other half, yielding 28 non-redundant terms.

The 8 dc terms are shown in FIG. 4 as a single vector sum, labeledI_(dc), while the 28 interference terms are shown in FIG. 4 as a singlevector, labeled I_(i). These vectors I_(dc) and I_(i) are plotted in acomplex plane. Upon rotation of the fiber loop 16 (FIG. 1) thephase-dependent vector I_(i) rotates, in the manner of a phasor, throughan angle equal to the rotationally reduced phase difference φ_(s) due tothe Sagnac effect. The projection of the interference vector I_(i) uponthe real axis, when added to the vector I_(dc), yields the total opticalintensity I_(DET) of the optical output signal W₀, as measured by thedetector 20 (FIG. 1). In FIG. 5, this optical intensity I_(DET) isplotted as function of the Sagnac phase difference φ_(s), as illustratedby the curve 52.

As indicated above in reference to FIG. 2, cross coupling between themodes i and j can cause the fiber loop 16 to be nonreciprocal, resultingin a nonrotationally induced phase difference between the abovedescribed electric field components, and yielding an accumulated phaseerror φ_(e), which is indistinguishable from the rotationally inducedSagnac phase difference φ_(s). The phase error φ_(e) causes the phasorI_(i) to be rotated, e.g., from the position shown in solid lines to theposition shown in dotted lines in FIG. 4. This results in the curve 52of FIG. 5 being transalated by an amount φ_(e) e.g., from the positionshown in solid lines to the position shown in dotted lines in FIG. 5.

Elimination or reduction of the accumulated phase error φ_(e) requiresan analysis of the 28 interference terms resulting from superposition ofthe 8 electric field components discussed in reference to FIG. 2. At theoutset, it will be recognized that interference between electric fieldcomponents E_(is) ⁺ with E_(is) ⁻, and E_(js) ⁺ with E_(js) ⁻, result inno phase error contribution, since the light represented by thesecomponents is not cross coupled, and traverses the loop in a single oneof the modes. However, the remaining 26 interference terms cancontribute to the accumulated phase error φ_(e). These 26 interferenceterms correspond to 26 pairs of electric field components which may beclassified into 3 groups, namely, Group I, Group II, and Group III, asfollows:

    ______________________________________                                        Group I             Group II                                                  E.sub.is.sup.+  and E.sub.ic.sup.+                                                                E.sub.is.sup.+  and E.sub.jc.sup.-                        E.sub.is.sup.+  and E.sub.ic.sup.-                                                                E.sub.is.sup.+  and E.sub.js.sup.-                        E.sub.is.sup.-  and E.sub.ic.sup.+                                                                E.sub.is.sup.+  and E.sub.jc.sup.+                        E.sub.is.sup.-  and E.sub.ic.sup.-                                                                E.sub.is.sup.+  and E.sub.js.sup.+                        E.sub.js.sup.+  and E.sub.jc.sup.+                                                                E.sub.ic.sup.+  and E.sub.jc.sup.-                        E.sub.js.sup.+  and E.sub.jc.sup.-                                                                E.sub.ic.sup.+  and E.sub.js.sup.-                        E.sub.js.sup.-  and E.sub.jc.sup.+                                                                E.sub.ic.sup.+  and E.sub.jc.sup.+                        E.sub.js.sup.-  and E.sub.jc.sup.-                                                                E.sub.ic.sup.+  and E.sub.js.sup.+                        Group III           E.sub.ic.sup.-  and E.sub.jc.sup.-                        E.sub.ic.sup.+  and E.sub.ic.sup.-                                                                E.sub.ic.sup.-  and E.sub. js.sup.-                       E.sub.jc.sup.+  and E.sub.jc.sup.-                                                                E.sub.ic.sup.-  and E.sub.jc.sup.+                                            E.sub.ic.sup.-  and E.sub.js.sup.+                                            E.sub.is.sup.-  and E.sub.jc.sup.-                                            E.sub.is.sup.-  and E.sub.js.sup.-                                            E.sub.is.sup.-  and E.sub.jc.sup.+                                            E.sub.is.sup.-  and E.sub.js.sup.+                        ______________________________________                                    

Although only the intefering electric field components are listed above,and not the interference terms themselves, it will be understood thatthe interference term for each of the above listed pairs of componentsmay be readily calculated in accordance with the example provided inreference to equation (1).

Group I, includes those pairs of field components, which originated indifferent modes, bhut which are in the same mode upon reaching thecoupler 14, after traversing the loop 16. For example, the first ofGroup I pair of components comprises a straight-through component E_(is)⁺, which originated in mode i and remained in mode i during traverse ofthe loop 16, and a cross coupled component E_(ic) ⁺ which originated inmode j but was cross coupled to mode i during traverse of the loop 16.Ordinarily, these components would interfere with each other, asdescribed in reference to equation (1).

However, since the phase difference between incoherent light waves israndom, interference between incoherent light wave components will beaveraged to zero in the detector 20. Accordingly, Group I interferenceterms can be eliminated by insuring that each mode is launched withlight that is incoherent, i.e., random in phase with respect to thelight in the other modes. Thus, for example, if mode i is launched withlight that is incoherent with respect to light in mode j, the averageinterference between, e.g., the components E_(is) ⁺ and E_(ic) ⁺, willbe zero, since the phase difference therebetween is random, andtherefore, will be averaged to zero in the detector 20. Similarly, theinterference between the remaining components, e.g., E_(is) ⁺ and E_(ic)⁻ ; E_(is) ⁻ and E_(ic) ⁺ ; etc., will be averaged to zero. Accordingly,by utilizing the incoherent source 10, described above, interferencebetween the components listed in Group I and thus, phase errors causedby such interference, may be reduced or eliminated.

The degree of incoherence necessary to reduce Group I phase errors is afunction of the optical path length difference between modes. To theextent that the coherence length of the source light is less than theoptical path length difference between two given modes, the averageinterference between Group I components for those two modes, and thus,the phase error, will be reduced. For the case of N modes, a reductionin phase error will begin to occur when the coherence length of thelight source is less than the difference between the longest opticalpath and the shortest optical path. However, for essentially completeelimination of Group I errors, the coherence length should be less thanthe smallest optical path difference between modes.

The relationship between the accumulated phase error φ_(e)(I) due toGroup I terms and the coherence length may be approximated bydetermining the number of all possible combinations of mode pairs(including gneralized polarization modes as well as fundamental modes)in which the coherence length is greater than the optical path lengthdifference. This number will be referred to as "K". The phase errorφ_(e)(I) is then: ##EQU1## Where N is the number of modes, includingboth fundamental and generalized polarization modes.

For example, for a fiber having N=3,000 modes, the number of path lengthcombinations would be N(N-1), or (3,000)² which yields 9,000,000possible combinations. If 1% of these path length combinations have apath length difference which is greater than the coherence length of thesource: ##EQU2## Thus, the error contribution due to Group I errors inthis example is only 10⁻² radians. For most practical applications, thetotal phase error φ_(e) as an order of magnitude, should be no greaterthan this value, e.g., 10⁻² radians. Substituting this value in equation(2) yields:

    k≦0.01N.sup.2                                       (4)

Accordingly, the coherence length of the source 10 should be selected tosatisfy equation (4). However, in general, the shorter the coherencelength, the smaller the Group I phase error will be.

It will be understood by those skilled in the art that the optical pathlengths of the fiber modes may be measured or calculated, using modaldispersion data provided by the manufacturer of the fiber.

Group II includes those pairs of electric field components which are indifferent modes, after traverse of the loop 16, regardless of the modein which they originated. Thus, for example, field component E_(is) ⁺,in mode i is paired with component E_(jc) ⁻, in mode j. Since the modes,e.g., i, j, are orthogonal, and since the electric fields of orthogonalmodes do not interfere, there will be no interference between the termsin Group II. It is important to recognize, however, that the fieldpatterns of the paired electric fields in Group II are only orthogonalin a "global" sense. That is, the entire field patterns must bespatially averaged over a plane normal to the fiber axis to eliminateinterference. If such spatial averaging is accomplished for only aportion of the field patterns, orthogonality may not exist. To ensurethat substantially the entire field patterns of, e.g., the modes i and jare spatially averaged, the present invention utilizes a detector 20which has a surface area sufficiently large to capture substantially allof the light exiting the end of the fiber 19, as discussed above.

Only two interference terms result from the pairs of electric fieldcomponents listed in Group III, namely, an interference term resultingfrom superposition of the component E_(ic) ⁺ with E_(ic) ⁻, and anotherinterference term resulting from superposition of the components E_(jc)⁺ with E_(jc) ⁻. Thus, each interference term results from a pair ofcomponents, one of which originated in a first mode and, during traverseof the loop 16 was cross coupled to a second mode, while the otheroriginated in that same first mode and was cross coupled to the samesecond mode, but traversing the loop 16 in the opposite direction. Theseinterference terms, while being only two in number, are highly sensitiveto the environment and can result in a phase error which may be ordersof magnitude larger than the Sagnac phase difference.

The interference between E_(ic) ⁺ and E_(ic) ⁻ yields a phase dependentterm:

    -1/4η.sub.ij.sup.2 |E.sub.j |.sup.2 cos (φ.sub.s +φ.sub.p -φ.sub.q)                                (5)

Similarly, the interference between E_(jc) ⁺ and E_(jc) ⁻ yields a phasedependent term:

    -1/4η.sub.ij.sup.2 |E.sub.i |.sup.2 cos [φ.sub.s -(φ.sub.p -φ.sub.q)]                              (6)

Where η_(ij) is the fraction of the electric field energy that iscoupled between the i and j modes; η_(ij) ² is the fraction of theoptical intensity that is coupled between the i and j modes; φ_(s) isthe rotationally induced, Sagnac phase difference between the twocomponents; φ_(p) is the total accumulated phase for light that is crosscoupled from one mode to another between the terminals C" and D'; φ_(q)is the total accumulated phase for light that is cross coupled from onemode to the other between terminals C' and D".

The vectors corresponding to these interference terms (5) and (6) areplotted in a complex plane in FIG. 6, as the vectors 56 and 58,respectively. It will be understood that the interference terms (5) and(6) are merely the projections of the vectors 56 and 58 respectively,upon the real axis. The vectors 56 and 58 may be vectorially added toyield a resultant vector 60, shown in FIG. 7. Note that, for clarity ofillustration, the Sagnac phase difference φ_(s) is assumed to be zero inFIGS. 6 and 7. As shown in FIG. 7, the vector 60 is inclined from thereal axis by a phase angle φ_(e)(III), which represents thenon-rotationally induced phase error due to interference between thecomponents of Group III. The projection of the vector 60 upon the realaxis is simply the algebraic sum of the two interference terms (5) and(6):

    -1/4η.sub.ij.sup.2 {|E.sub.j |.sup.2 cos (φ.sub.s +φ.sub.p +φ.sub.q)+|E.sub.i |.sup.2 cos [φ.sub.s-(φ.sub.p -φ.sub.q)]}                 (7)

Since the detector 20 measures only that component of the vector 60which is along the real axis, the detector 20 output will beproportional to the algebraic sum (7). Thus, it may be seen that thephase error φ_(e)(III) (FIG. 7) will cause a corresponding error in thedetector 20 output.

The algebraic sum (7) of the interference terms may be rewritten asfollows:

    -1/4η.sub.ij.sup.2 [(|E.sub.i |.sup.2 +|E.sub.j |.sup.2) cos (φ.sub.p -φ.sub.q) cos φ.sub.s +(|E.sub.i |.sup.2 -|E.sub.j |.sup.2 sin (φ.sub.p -φ.sub.q) sin φ.sub.s ](8)

Note that, if |E_(i) |² and |E_(j) |² are equal, this algebraic sum (8)reduces to:

    -1/2η.sub.ij.sup.2 |E|.sup.2 cos (φ.sub.p -φ.sub.q) cos φ.sub.s                             (9)

In this form, the effect of variations in the quantity φ_(p) -φ_(q) canbe distinguished from the rotationally induced Sagnac phase differenceφ_(s), as may be more fully understood through reference to FIGS. 8 and9, which show the effect, upon the resultant vector 60, of making thevectors 56 and 58 equal in magnitude. It will be seen that, regardlessof the value of the quantity φ_(p) -φ_(q), the resultant vector 60 willalways be directed along the real axis, and thus, the direction of thevector 60 is independent of variations in the quanitity φ_(p) -φ_(q).Although such variations will cause the vector 60 to fluctuate inmagnitude, such fluctuations do not affect the detector 20 outputsubstantially, since, as will be discussed hereinafter, these magnitudefluctuations will be averaged with corresponding magnitude fluctuationsfrom many other modes of the multimode fiber, so that the sum total ofall such fluctuations tend towards zero.

Accordingly, to the extent that the intensity of the light in each modeis launched with light having an intensity equal to that of the othermodes, phase errors due to Group III terms will be eliminated.Preferably, the light in the modes should be equalized with respect tointensity by the time it reaches the coupler 14 and is split into thecounterpropagating waves so that the Group III interference terms havethe proper magnitudes and phase angles in cancellation of the phaseerror at the detector 20. Further, all of the mode should be launched bythe time the light is split at the coupler 14, since to the extent thata mode does not have any light intensity, the modes will not beequalized with respect to intensity, thereby producing Group III phaseerrors. Of course, even if all the modes are not launched, there willstill be some reduction of Group III phase errors so long as some of theplural modes are substantially equalized in intensity. As discussedabove, the present invention utilizes a light-emitting diode (LED) toequally distribute the optical intensity among all of the fiber modes.

The above analysis may be applied to every combination of mode pairswithin the multimode fibers, with the same results, namely theelimination of phase errors. Further, when many modes are utilized, theenvironmental sensitivity of the detected optical signal tends todiminish. In this regard it will be recalled, from the discussion inreference to FIGS. 4 and 5, that the total optical intensity (I_(DET)),as measured by the detector 20, is:

    I.sub.DET =I.sub.dc+I.sub.i cos φ.sub.s                (10)

Assuming that the modes are launched with light having electric fields(E) that are equal in amplitude, I_(dc) is simply: ##EQU3## where N isthe number of fiber modes, including both fundamental modes andgeneralized polarization modes.

Further, assuming that the light in each mode is incoherent with respectto all other modes, and that the detector 20 has sufficient surface areato ensure global orthogonality, so that Group I and Group IIinterference terms are zero, the interference term I_(i) cos φ ofequation (10) may be expressed as: ##EQU4## where: η_(ku) ² is thefraction of the optical power coupled from either the k^(th) mode to theu^(th) mode, or from the u^(th) mode to the k^(th) mode. ξ_(k) ² is theuncoupled fraction of such optical power, which remains in a given mode,e.g., the k^(th) mode, without cross coupling.

Further, φ_(ku) is the difference in the total accumulated phase (1)light originating in the one mode k, u, which is cross coupled to theother mode k, u, and which traverses the loop 16 in the plus (+)direction, and (2) light originating in that same one mode k, u, whichis cross coupled to that same other mode k, u, but which traverses theloop 16 in the other or minus (-) direction. For the above discussionrelating to modes i, j (FIG. 2), the phase angle φ_(ku) is equal to thequantity φ_(p) -φ_(q).

The first term on the right hand side of equation (12) is simply theoptical intensity resulting from the sum of the interference termsassociated with "straight through" lightwave components (e.g., E_(is) ⁺,E_(js) ⁺, E_(is) ⁻, and E_(js) ⁻).

Although these "straight through" components, as discussed above, do notresult in phase errors, they nevertheless interfere in response to therotationally induced "Sagnac" phase difference. The remaining term onthe right hand side of equation (12) is the optical intensity resultingfrom the sum of interference terms associated with Group III components.(Compare equation (12) with equation (9)) It will be recalled that suchinterference terms do not result in a phase error so long as all themodes have equal intensities.

Equation (12) may be rewritten as follows: ##EQU5## where I_(T) =N|E|².From equation (13), it may be seen that both the "straight through"interference terms and the Group III, "cross coupling" interferenceterms are summed over the N modes, and then are divided by N, so thatthey may be viewed as being averaged over the N modes. If there are manymodes, changes in ξ and η, due to perturbations of the fiber, will beaveraged, yielding a more stable signal. The stability of the signal isproportional to 1/√N.

In addition, it should be noted that the phase angle φ_(ku) may have anyvalue betwen 0° and 360°, and that this value may be either positive ornegative. Therefore, as the number of modes increases, the average valueof cos φ_(ku) tends towards zero, thus reducing equation (13) to:##EQU6## In practice, it has been found that: ##EQU7## and that:

    I.sub.dc ≈1/2I.sub.T                               (16)

Substituting equation (15) into equation (14), and equations (14) and(15) into equation (10) yields:

    I.sub.DET =1/2I.sub.T (1+1/2 cos φ.sub.s)              (17)

Thus, the intensity of the optical output signal W₀, as measured by thedetector 20, will vary in response to the rotationally induced Sagnacphase difference φ_(s), as shown by the curve 52 in solid lines in FIG.5. By eliminating Group I, II, and III phase errors, the totalaccumulated phase error φ_(e) is zero, so that the curve 52 will remainstable with respect to phase, e.g., without translation along the φ_(s)axis in FIG. 5. Further, the amplitude of the curve 52 tends to remainstable, substantially insensitive to changes in birefringence caused byenvironmental factors, since the remaining interference terms areaveraged over the N modes of the fiber. The stability of the curve 52amplitude is proportional to 1√N.

The rotation sensor of the present invention also advantageously reducesthe effects of light which is backscattered in the fiber loop. In thisregard, it will be recognized that present state-of-the-art opticalfibers are not optically perfect, but have imperfections which causescattering of small amounts of light. This phenomena is commonlyreferred to a Rayleigh scattering. Although such scattering causes somelight to be lost from the fiber, the amount of such loss is relativelysmall, and thus, is not a major concern. The principal problemassociated with Rayleigh scattering relates to the portion of the lightwhich is reflected so that it propagates through the fiber in adirection opposite to its original direction of propogation. This iscommonly referred to as "backscattered" light. To the extent that suchbackscattered light is coherent with light traveling in the samedirection around the loop 16, it can constructively or destructivelyinterfere therewith, and thereby cause variation in the intensity of theoptical output signal W₀, as measured by the detector 20. Suchinterference is reduced in the present invention by utilizing the source10, which permits launching of each mode with light that is incoherentwith respect to the other modes. Thus, backscattered light originatingfrom e.g., mode i, but captured by another mode, e.g. mode j, will notinterfere with light in that other mode, e.g. mode j. Further, when thelight waves are recombined at the coupler 14, the light in e.g. mode iwill not interfere with backscattered light that originated in mode iand was captured by another mode, e.g. mode j, since the modes areorthogonal. Consequently, the only backscattered light which can causeinterference is that backscattered light which originated in aparticular mode and remained in that same mode during traverse of theloop 16. In effect, the backscattered light is averaged over theN-modes, so that the amount of interference from backscattered light isinversely proportional to the number of modes. Accordingly, forreduction of back scatter, it is preferable to use a fiber having alarge number of modes.

A second embodiment of the present invention shown in FIGS. 1 and 10,utilizes a bidirectional modal filter, which passes a single mode (i.e.,a single one of the generalized polarization modes within a particularfundamental mode), while rejecting light in all other modes. In thepreferred embodiment, a modal filter comprises a transmissive hologram70, which is located within the optical path of the fiber 11, betweenthe couplers 12 and 14, so that the input light wave W_(i) travelsthrough the filter 70 on the way to the loop 16, and the outputlightwave W₀ travels through this same filter on its way to the detector20. Referring to FIG. 10, this filter 70 is placed in the optical pathof the fiber 11 by severing the continuous strand of fiber 11, at thedesired location, between the couplers 12 and 14, to provide two fiberportions 11a and 11b. The filter 70 is then placed between the fiberportions 11a and 11b, so as to intercept the input wave W_(i) and outputwave W₀.

Those skilled in the art will recognize that such a holographic filter70 may be made by utilizing a technique illustrated in FIG. 11. As showntherein, this method utilizes a pair of multimode fibers 80, 82,identical to the fiber portions 11a and 11b, respectively, except thatthey are very short in length (e.g., 10 cm.). The pair of fibers 80, 82and a holographic plate 84 are relatively positioned in the exact manneras desired for the fiber portions 11a, 11b, and filter 70. The desiredsingle mode (i.e., the mode to be transmitted by the filter 70) of thepair of fibers 80, 82 is launched with a pair of light waves W_(a),W_(b), respectively, both of which are directed to propagate towards theplate 84, so that light exiting from the fibers 80, 82 is intercepted bythe holographic plate 84. In the embodiment shown, the fibers 80, 82 areoriented so that the waves W_(a), W_(b) strike the plate from oppositesides thereof, and cover exactly the same area of the plate 84. Afterexposure of the holographic plate 84 in such manner, the plate isdeveloped and placed between the fiber portions 11a and 11b, to providethe filter 70. To the extent that the filter 70 and fiber portions 11a,11b are relatively positioned exactly as were the holographic plate 84and pair of fibers 82, 84 used during manufacture of the filter 70, thefilter 70 will pass only the desired single mode, rejecting all othermodes.

The elimination of phase errors through use of the modal filter 70 maybe more fully understood through reference to the conceptual model ofthe modes i and j, discussed in reference to FIG. 2. In this regard, itwill be assumed that the filter 70 passes light in mode i, whilerejecting all other modes, e.g., modes j. Accordingly, after the inputlightwave W_(i) passes through the filter 70, the only field componententering the fiber portion 11b (FIG. 10) will be E_(i). During traverseof the loop 16, mode mixing will occur, due to cross coupling betweenthe modes, so that, when the counter propogating waves are recombined atthe coupler 14 to form the optical output signal W₀, only theinterference terms corresponding to the following pairs of electricfield components will exist:

E_(is) ⁺ and E_(is) ⁻

E_(is) ⁺ and E_(jc) ⁺

E_(is) ⁻ and E_(jc) ⁻

E_(is) ⁺ and E_(jc) ⁻

E_(is) ⁻ and E_(jc) ⁺

E_(jc) ⁺ and E_(jc) ⁻

As the optical output signal W₀ passes through the filter 70, from thefiber portion 11b to the fiber portion 11a (FIG. 10) all of thecomponents having a "j" subscript are eliminated, leaving only theinterfering components E_(is) ⁺ and E_(is) ⁻. Since interference betweenthis pair of components does not contribute to phase errors, there willbe no phase errors in the optical output signal W₀ as measured by thedetector 20. Although the optical output signal W₀ of this secondembodiment will be substantially decreased in intensity compared to thatof the first-described embodiment, due to use of only a single mode ofthe multimode fiber, this second embodiment, like the first embodiment,is advantageous in that it permits use of relatively inexpensivemultimode fiber.

What is claimed is:
 1. A multimode fiber optic rotation sensor,comprising:light source means for producing a light wave; a multimodeoptical fiber which supports plural spatial modes for said lightwave,said fiber forming a loop for sensing rotation in accordance with theSagnac effect; a device for splitting said light wave into a pair oflight waves which propagate about said loop in opposite directions, theintensity of each of said lightwaves distributed substantially equallyamong substantially all of the modes of said fiber, said loop configuredto return said pair of light waves to said splitting device afterpropagation through said loop, said splitting device combining said pairof light waves to form an optical output signal comprised of light fromsubstantially all of the modes of said fiber; means for detecting saidoptical output signal to determine the rotation rate of said loop, saiddetecting means detecting light from substantially all of the modes ofsaid fiber.
 2. A rotation sensor, as defined by claim 1, wherein saidlight source means launches plural modes of said fiber, and wherein eachmode of said multimode fiber is launched with light which issubstantially incoherent with respect to the light launched into theother modes.
 3. A rotation sensor, as defined by claim 2, wherein thecoherence length of light produced by said light source means is suchthat: K≦0.01 N² where: N is the number of propagation modes of saidmultimode fiber for said light source; and K is the number of pairs ofsuch modes in which the optical path length difference in said loop isless than said coherence length.
 4. A rotation sensor, as defined byclaim 2, wherein said light source means comprises a light emittingdiode.
 5. A rotation sensor, as defined by claim 2, additionallycomprising means for phase modulating light produced by said lightsource means.
 6. A rotation sensor, as defined by claim 5, wherein saidphase modulating means is driven at a random frequency.
 7. A rotationsensor, as defined by claim 5, wherein said phase modulating means isdriven at a frequency outside the bandwidth of said detecting means. 8.A rotation sensor, as defined by claim 5, wherein said phase modulatingmeans is located between said light source means and said splittingdevice.
 9. A rotation sensor, as defined by claim 1, wherein saidsplitting device comprises a fiber optic directional coupler.
 10. Arotation sensor, as defined by claim 1, wherein said detecting meanscomprises a detector which intercepts substantially the entire saidoptical output signal.
 11. A rotation sensor, as defined by claim 10,wherein said light source means comprises a light emitting diode.
 12. Arotation sensor, as defined by claim 1, additionally comprising a modescrambler for equalizing the respective intensities of said light insaid plural modes.
 13. A rotation sensor, comprising:a light source forproducing light; detector means for detecting said light; multimodefiber means forming a fiber loop for providing a multimode optical pathfor propagation of said light (1) from said source to said loop and (2)from said loop to said detector means; and a hologram, disposed in saidmultimode optical path, said hologram passing light from only a singlegeneralized polarization mode within said multimode optical path, whileblocking light from all other modes of said multimode optical path. 14.A multimode fiber optic rotation sensor, comprising:a light source forproducing a lightwave; a multimode optical fiber which supports pluralspatial modes for light produced by said light source, said fiberforming a loop for sensing rotation, said lightwave propagating to saidloop along a selected light path; a splitting device for receiving saidlightwave propagating along said selected light path and for splittingsaid lightwave into two lightwaves, said splitting device coupling saidtwo lightwaves to said loop for counterpropagation about said loop, theintensity of said two lightwaves substantially equally distributed amongthe modes of said fiber, said splitting device combining said two lightwaves after propagation through said loop to form an optical outputsignal comprised of light from substantially all of said modes andoutputting said optical output signal for propagation along saidselected light path; a detector for detecting said optical signal; andmeans for coupling said detector to receive light from said selectedlight path.
 15. In a Sagnac interferometer, a method of sensingrotation, comprising:utilizing a splitting device to split a lightwaveinto a pair of lightwaves; coupling said pair of light waves tocounterpropagate through a multimode fiber loop formed from a multimodefiber which supports plural spatial modes for said lightwaves; saidequalizing the light intensity of each of said light waves amongsubstantially all of the modes of said multimode fiber; rotating saidmultimode fiber loop to induce a phase difference between said lightwaves, in accordance with the Sagnac effect; utilizing said splittingdevice to combine said light waves after propagation through said loopto form an optical output signal; impressing said optical output signalupon a detector; reducing nonrotationally induced phase differencesbetween said counter-propagating waves by selecting said detector tohave a sufficiently large surface area to intercept substantially theentire said optical output signal.
 16. In an interferometer having twomultimode optical paths comprised of multimode fiber which supportsplural modes, a method of sensing rotation, comprising:passing alightwave through a splitting device to form a pair of light waves;coupling said pair of light waves to propagate through said multimodefiber optical paths; reducing nonrotationally induced phase differencesbetween said light waves by launching each of said plural modes of saidmultimode fiber, for both of said optical paths, with light that is (1)substantially incoherent with respect to light launched in the othersaid plural modes of said multimode fiber and (2) substantially equal inintensity with respect to light launched in the other of said pluralmodes of said multimode fiber; passing said pair of light waves throughsaid splitting device to combine said waves to form an output signal;and detecting said output signal to determine the phase differencebetween said light waves.
 17. In a Sagnac interferometer, a method ofsensing rotation, comprising:passing a light wave through a splittingdevice to form a pair of light waves; coupling said pair of light wavesto propagate through a multimode optical fiber loop formed from amultimode fiber which supports plural spatial modes for said lightwaves; reducing non-rotationally induced phase differences between saidlight waves by launching each of said plural modes of said multimodefiber with light that is substantially incoherent with respect to lightlaunched in the other said plural modes of said multimode fiber; passingsaid pair of light waves through said splitting device to combine saidwaves to form an output signal; and producing said light wave utilizinga light source having a coherence length such that:

    K≦0.01N.sup.2

where N is the number of modes of said multimode fiber, and K is thenumber of mode pairs in which the optical path length difference betweenthe mode pairs is less than said coherence length.
 18. In a Sagnacinterferometer, a method of rotation sensing comprising:passing a lightwave through a splitting device to form a pair of light waves; couplingsaid pair of light waves to counterpropagate through a fiber loop formedfrom a multimode optical fiber which supports plural spatial modes forsaid lightwaves; reducing nonrotationally induced phase differencesbetween said pair of light waves by substantially equalizing theintensity of light in the modes of said multimode fiber for both of saidlight waves; passing said light waves through said splitting device tocombine said waves to form an output signal; and detecting said outputsignal.
 19. In a Sagnac interferometer, a method of sensing rotation, asdefined by claim 18, wherein said reducing step comprises coupling lightfrom a light emitting diode to said fiber.
 20. In a Sagnacinterferometer, a method of sensing rotation, comprising:passing a lightwave through a splitting device to form a pair of light waves; couplingsaid pair of light waves to counterpropagate through a fiber loop formedof multimode optical fiber which supports plural spatial modes for saidlight waves; and reducing non-rotationally induced phase differencesbetween said pair of light waves by passing said light wave through amode scrambler to substantially equalize the intensity of light in themodes of said multimode fiber.
 21. In a Sagnac interferometer, a methodof sensing rotation, comprising:passing a light wave through a splittingdevice to form a pair of light waves; coupling said pair of light wavesto propagate through a multimode fiber loop, formed from a multimodefiber which supports plural spatial modes for said light waves; reducingnonrotationally induced phase differences between said pair of lightwaves by launching each of said lightwaves into said multimode fiberloop such that:(1) each of said plural modes of said multimode fiber islaunched with light that is substantially incoherent with respect tolight launched in the other of said plural modes of said multimodefiber; (2) the intensity of the light is substantially equalized amongthe modes of said multimode fiber; and passing said pair of lightwavesthrough said splitting device to combine the lightwaves afterpropagation through said loop to form an optical output signal.
 22. In aSagnac interferometer, a method of sensing rotation, as defined by claim21, wherein said reducing step additionally comprises:selecting adetector having a sufficiently large surface area to interceptsubstantially the entire said optical output signal; and positioningsaid detector to intercept substantially the entire said optical outputsignal.
 23. A rotation sensor comprising a coil of multimode opticalfiber, means for applying two lightwaves in opposite directions throughsaid coil, such that the optical power for each of said lightwaves issubstantially evenly divided among the modes of said multimode fiber,and means for detecting substantially all of the modes of said twolightwaves after passing through said coil.
 24. A method of sensingrotation including the steps of providing a coil of multimode opticalfiber, applying two lightwaves in opposite directions through said coilsuch that the optical power for each of said two lightwaves issubstantially even divided among the modes of said multimode fiber, anddetecting substantially all of the modes of said two lightwaves afterpassing through said coil.
 25. The method as defined by claim 24 andfurther including the step of shifting the phase of one of saidlightwaves relative to the other lightwave.
 26. An interferometer havingtwo multimode optical paths formed of multimode fiber, comprising:meansfor applying a pair of lightwaves to said multimode fiber forpropagation through said two multimode optical paths, said applyingmeans including means for substantially equalizing the intensity of eachof said pair of waves among substantially all of the modes of saidmultimode fiber; means for combining said lightwaves to form an opticalsignal comprised of light from substantially all of the modes of saidmultimode fiber; and means for detecting the entire said optical outputsignal.
 27. An interferometer, as defined by claim 26, wherein said twooptical paths are formed by a single loop comprised of said multimodeoptical fiber.
 28. A method of sensing rotation, as defined by claim 24,additionally comprising the step of providing a light source forproducing spatially coherent light, and wherein the applying stepcomprises passing said coherent light through a phase modulator formodulating the phase of said light, said modulator acting as a modescrambler to distribute light substantially evenly among the modes ofthe fiber.
 29. A rotation sensor, as defined by claim 23, additionallycomprising a light source for producing spatially coherent light, andwherein said applying means comprises a phase modulator for modulatingthe phase of said light, said phase modulator acting as a mode scramblerto distribute light substantially evenly among the modes of said fiber.30. A rotation sensor, as defined by claim 23, wherein said applyingmeans comprises light source means which produces light having acoherence length less than the optical path length difference betweentwo modes of said loop of optical fiber.
 31. A rotation sensor, asdefined by claim 30, wherein said coherence length is less than theshortest optical path length difference between two modes of said loopof optical fiber.